Central configurations play an important role in the (Newtonian) \(n\) -body problem: to name two, they arise as configurations yielding homographic solutions, and as rest points in the flow on the McGehee collision manifold. Following the spirit of Albouy and Chenciner [1]}, in this article we study the problem of central configurations from the point of view of mutual distances; but instead of lengths we consider the space of differences of positions, which turns out to be a suitable group of cochains \(C^1\)  of degree 1 with coefficients in the Euclidean space \(E\) . Hence, we show that central configurations are critical points of a function defined on \(C^1\)  and restricted to the subspace of 1-cocycles, and show some consequences. The technique of embedding the central configurations problem into a suitable space of cocycles was actually already used by Moeckel in [2]}, in an implicit way, and again by Moeckel and Montgomery in [3]}. In this article we study this approach introducing cocycles and cohomology, and show that many calculations can be significantly simplified in this way. For further details and recent remarkable advances we refer to [4]}, [5]}.
